The present invention is directed to a method of analyzing a sample by use of a QUISTOR mass spectrometer.
The "QUISTOR" (QUadrupole Ion STORe") or "ion trap" can store ions of different mass-to-charge ratios simultaneously in its radio-frequency hyperbolic three-dimensional quadrupole field.
The QUISTOR consists of a toroidal ring electrode and two end cap electrodes. A high RF voltage of amplitude V.sub.stor and frequency f.sub.stor is applied between the ring electrode and the two end caps. Both end cap electrodes normally are connected to the same potential. The radio-frequency voltage across the electrodes forms, at least near the center of the QUISTOR, a hyperbolic three-dimensional quadrupole field which is able to trap ions.
Cylindrical coordinates are used to describe the QUISTOR. The direction from the center towards the saddle line of the ring electrode is called the r direction or r plane. The z direction is defined to be normal to the r plane.
The ion oscillations by the RF field cause, integrate over time, a resulting force towards the center, and proportional to the distance from the center. This quasi-elastic central force field forms, integrated over time, an harmonic oscillator for the ions. The relatively slower harmonic oscillations around the center are superimposed by the faster impregnated RF oscillations.
The harmonic oscillations are called the "secular" oscillations of the ions within the QUISTOR field.
The exact mathematical description of the movements of ions in a QUISTOR is difficult. Up to now, a solution of the resulting partial equations was only possible for the special case of independent secular movements in r and z directions. The solution of the corresponding "Mathieu"'s differential equations results in an "ideal QUISTOR" of fixed design: The slope of the asymptotic cone envelope has the "ideal angle" z/r=1/1.414 (1.414=square root of 2).
Most of the QUISTORs which have been built up to now, follow the design principles of such an "ideal QUISTOR" with hyerbolic surfaces and the above "ideal" angle z/r, although it has been shown experimentally that QUISTORs of quitely different design, e.g. with cylindrical surfaces do store ions by no means less effective.
In the special case of an "ideal QUISTOR", the secular oscillations are, by the inherent mathematical assumptions, independent, and different, in r and z directions. The stability area boundaries for the ion movements in the well-known a/q diagram can be calculated. The stability area is formed by a net of beta.sub.r lines (0&lt;beta.sub.r &lt;1) and crossing beta.sub.z lines (0&lt;beta.sub.z &lt;1). The beta lines describe exactly the secular frequencies: EQU f.sub.sec,r =beta.sub.r * f.sub.stor /2; EQU f.sub.sec,z =beta.sub.z * f.sub.stor /2.